The effect of transverse stresses on the structure of two-dimensional flows in a uniform field

The rotational viscosity mechanism leads to that the total tensor of viscous stresses becomes an anisotropic function of the deformation rate tensor. The anisotropy induced by the field may stipulate an essential rearrangement of the structure of ferrohydrodynamic flows when the field is applied. Such a rearrangement may be exemplified by the generation of perturbations by the plate oscillating in its plane in the fluid normal to the plate direction. On the other hand, the application of a uniform field of random orientation does not change the structure of the Couette flow or the Poiseuille flow in an elliptical tube. The problems as to which of these phenomena is most widely encountered may be solved when studying flows more complex than one-dimensional flows. In this chapter, this problem is solved within the model of two-dimensional flows the characteristics of which are constant along some linear axis. In the Newtonian fluid there are two types of motion of such a structure. They are plane and axial flows with the velocity vectors, correspondingly normal and parallel to the axis. Because of the isotropic nature of the Newtonian tensor, viscous friction forces for plane motions lie in the same plane as the velocity vector; in case of axial flows, they are directed along the flow. Therefore, plane and axial flows may exist independently